Question

If the unit of force and length each be increased by four times, then the unit of energy is increased by:

• A. $16times$
• B. $8times$
• C. $2times$
• D. $4times$

Answer 1

The correct option is A

$16times$

Step 1: Given data

Initial force: $F_1=F$

New force: $F_2=4F$

Initial length $L_1=l$

New length: $L_2=4l$

Step 2: Formula used

$E=W=Fd$

Step 3: Find the increase in energy

Calculate the initial energy using the formula. Here, work done is energy, and length is displacement.

$\begin{array}{rcl}E& =& FN\times lm\\ & =& FlNm..........\left(1\right)\end{array}$

Calculate the new energy using the formula. Here, work done is energy and length is displacement.

$\begin{array}{rcl}E& =& 4FN\times 4lm\\ & =& 16FlNm............(From1)\\ & =& 16E\end{array}$

Hence, energy increases by $16times$.